The possible drops are listed on each monster's page. In addition there are several factors that influence the possible drop items and their amount:

Monster magazines

You can get magazines for each monster family ("Family Weekly" and "The Daily Family") by fulfilling guild tasks. Certain items will only be dropped when you have the corresponding magazine.

Location

Monsters that can be found on multiple location might have different drop lists for each location. Therefore move to a different location when you don't get the drop you are searching for.

Rarity

Some items are common drops, others are rare. Only patience helps here.

Number of enemies in the fight

Fighting multiple enemies at once (link them with Timeshift) results in higher numbers of dropped items. They do not have to be the same enemy. You get the same increase for timeshifting 2 dragons together as you do one dragon and one spider.

Each monster in every location can have up to 4 different normal drops and 2 item specific drops. This can different for the same monster in different locations, or even within the same location, as is the case for union leader monsters, they often have rare drops the other monsters don't, or simply drop a higher quantity of the same items. If the monster can be captured, one of the four regular drops will be the captured monster instead.

When a killing blow is being dealt to a monster the game immediately calculates the items dropped. This is because most smaller monsters will stay on the battlefield rather than disappearing when they are captured.

Monster drops have 4 different rarity categories: Common (45% base drop chance), Uncommon (30% base drop chance), Rare (15% base drop chance), and Very rare (3% base drop chance). Drop chances are affected by one thing, and one thing only: the number of monsters already killed in the battle. The game looks up this number, adds one to it (for the monster just being killed), and then uses the result to determine item drop chances. Common drops often have a minimum amount that will be dropped by a monster, especially for rare monsters, in this case you will never get less than this amount if the item drops.

Once the regular drops have been determined the two special drops are looked up. These require specific items to be in your inventory, like monster magazines. These drops have set percentage chances and are not affected by any other factors (ie monsters killed in the battle), however they can be (and sometimes are) different for the same monster in different locations.

When the battle ends, there can be further changes to the loot dropped, this, again, is based on the amount of monsters killed in the battle. In the table below this is represented by the Extra Loot columns, and it works like this: the first number is used to determine how many passes the game will make over the loot list, while the second is the maximum number of items that can be increased in a pass. For each of these, a random item on the list will get increased by one. Equippable items, captured monsters, and special items recieved as loot are ignored by this mechanic, but magazine drops can be increased.

If the battle yielded any Gold, this is multiplied based on the amount of monsters defeated as well.